Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard terms
In this paper, we consider the following Schrödinger equation with perturbations of Choquard terms: −Δu−λu=|u|4u+μ(Iα∗|u|p)|u|p−2u,x∈ℝ3,∫ℝ3u2dx=c, where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the Riesz potential with order [Formula: see text]. The ma...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2025-08-01
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| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360725500055 |
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| Summary: | In this paper, we consider the following Schrödinger equation with perturbations of Choquard terms: −Δu−λu=|u|4u+μ(Iα∗|u|p)|u|p−2u,x∈ℝ3,∫ℝ3u2dx=c, where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the Riesz potential with order [Formula: see text]. The main results in this paper are the following: (1)existence of ground state solution with negative energy for all [Formula: see text]; (2)existence of mountain-pass solution with positive energy for all [Formula: see text]; (3)existence of ground state solution for [Formula: see text] and some [Formula: see text]. |
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| ISSN: | 1664-3607 1664-3615 |